Generalized Pochhammer symbol

In mathematics, the generalized Pochhammer symbol of parameter $$\alpha>0$$ and partition $$\kappa=(\kappa_1,\kappa_2,\ldots,\kappa_m)$$ generalizes the classical Pochhammer symbol, named after Leo August Pochhammer, and is defined as


 * $$(a)^{(\alpha )}_\kappa=\prod_{i=1}^m \prod_{j=1}^{\kappa_i}

\left(a-\frac{i-1}{\alpha}+j-1\right). $$ It is used in multivariate analysis.